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      SUBROUTINE <a name="ZTREXC.1"></a><a href="ztrexc.f.html#ZTREXC.1">ZTREXC</a>( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          COMPQ
      INTEGER            IFST, ILST, INFO, LDQ, LDT, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      COMPLEX*16         Q( LDQ, * ), T( LDT, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZTREXC.18"></a><a href="ztrexc.f.html#ZTREXC.1">ZTREXC</a> reorders the Schur factorization of a complex matrix
</span><span class="comment">*</span><span class="comment">  A = Q*T*Q**H, so that the diagonal element of T with row index IFST
</span><span class="comment">*</span><span class="comment">  is moved to row ILST.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The Schur form T is reordered by a unitary similarity transformation
</span><span class="comment">*</span><span class="comment">  Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
</span><span class="comment">*</span><span class="comment">  postmultplying it with Z.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  COMPQ   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'V':  update the matrix Q of Schur vectors;
</span><span class="comment">*</span><span class="comment">          = 'N':  do not update Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix T. N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  T       (input/output) COMPLEX*16 array, dimension (LDT,N)
</span><span class="comment">*</span><span class="comment">          On entry, the upper triangular matrix T.
</span><span class="comment">*</span><span class="comment">          On exit, the reordered upper triangular matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDT     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array T. LDT &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Q       (input/output) COMPLEX*16 array, dimension (LDQ,N)
</span><span class="comment">*</span><span class="comment">          On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
</span><span class="comment">*</span><span class="comment">          On exit, if COMPQ = 'V', Q has been postmultiplied by the
</span><span class="comment">*</span><span class="comment">          unitary transformation matrix Z which reorders T.
</span><span class="comment">*</span><span class="comment">          If COMPQ = 'N', Q is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDQ     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array Q.  LDQ &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IFST    (input) INTEGER
</span><span class="comment">*</span><span class="comment">  ILST    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          Specify the reordering of the diagonal elements of T:
</span><span class="comment">*</span><span class="comment">          The element with row index IFST is moved to row ILST by a
</span><span class="comment">*</span><span class="comment">          sequence of transpositions between adjacent elements.
</span><span class="comment">*</span><span class="comment">          1 &lt;= IFST &lt;= N; 1 &lt;= ILST &lt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            WANTQ
      INTEGER            K, M1, M2, M3
      DOUBLE PRECISION   CS
      COMPLEX*16         SN, T11, T22, TEMP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.72"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.73"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="XERBLA.76"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>, <a name="ZLARTG.76"></a><a href="zlartg.f.html#ZLARTG.1">ZLARTG</a>, <a name="ZROT.76"></a><a href="zrot.f.html#ZROT.1">ZROT</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          DCONJG, MAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Decode and test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      WANTQ = <a name="LSAME.86"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( COMPQ, <span class="string">'V'</span> )
      IF( .NOT.<a name="LSAME.87"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( COMPQ, <span class="string">'N'</span> ) .AND. .NOT.WANTQ ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDT.LT.MAX( 1, N ) ) THEN
         INFO = -4
      ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN
         INFO = -6
      ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
         INFO = -7
      ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.101"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="ZTREXC.101"></a><a href="ztrexc.f.html#ZTREXC.1">ZTREXC</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.1 .OR. IFST.EQ.ILST )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      IF( IFST.LT.ILST ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Move the IFST-th diagonal element forward down the diagonal.
</span><span class="comment">*</span><span class="comment">
</span>         M1 = 0
         M2 = -1
         M3 = 1
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Move the IFST-th diagonal element backward up the diagonal.
</span><span class="comment">*</span><span class="comment">
</span>         M1 = -1
         M2 = 0
         M3 = -1
      END IF
<span class="comment">*</span><span class="comment">
</span>      DO 10 K = IFST + M1, ILST + M2, M3
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Interchange the k-th and (k+1)-th diagonal elements.
</span><span class="comment">*</span><span class="comment">
</span>         T11 = T( K, K )
         T22 = T( K+1, K+1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Determine the transformation to perform the interchange.
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="ZLARTG.135"></a><a href="zlartg.f.html#ZLARTG.1">ZLARTG</a>( T( K, K+1 ), T22-T11, CS, SN, TEMP )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Apply transformation to the matrix T.
</span><span class="comment">*</span><span class="comment">
</span>         IF( K+2.LE.N )
     $      CALL <a name="ZROT.140"></a><a href="zrot.f.html#ZROT.1">ZROT</a>( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS,
     $                 SN )
         CALL <a name="ZROT.142"></a><a href="zrot.f.html#ZROT.1">ZROT</a>( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS,
     $              DCONJG( SN ) )
<span class="comment">*</span><span class="comment">
</span>         T( K, K ) = T22
         T( K+1, K+1 ) = T11
<span class="comment">*</span><span class="comment">
</span>         IF( WANTQ ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Accumulate transformation in the matrix Q.
</span><span class="comment">*</span><span class="comment">
</span>            CALL <a name="ZROT.152"></a><a href="zrot.f.html#ZROT.1">ZROT</a>( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS,
     $                 DCONJG( SN ) )
         END IF
<span class="comment">*</span><span class="comment">
</span>   10 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="ZTREXC.160"></a><a href="ztrexc.f.html#ZTREXC.1">ZTREXC</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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